Crude Oil is pumped 799 miles across Alaska through a 1.22m diameter steel pipe

Question

Crude Oil is pumped 799 miles across Alaska through a 1.22m diameter steel pipe at a potential maximum rate of 2.4 million barrels a day. A more typical rate would be 1.8 million barrels a day. Using the typical pumping rate determine the horsepower needed to pump this oil through this system.

The temperature of the Crude Oil is 60oC
Its density is 860 kg m-3
And its viscosity is 3.83 × 10-3 kg s m-2
One barrel of oil is 0.1589837 m3 (42 gallons)

The volumetric flow rate of the oil is 3.313 m3 s-1


V=3.313/(p ?1.22?^2/4)=2.834 ms^(-1)



P_1/?g+(V_1^2)/2g+z_1+h_P=P_2/?g+(V_2^2)/2g+z_2+h_L


1 and 2 represent points within the large holding tanks at each end of the pipeline. h_P . Is the pressure head provided to the crude oil by the pumps.
Assume z_1=z_2 the crude oil is pumped from sea level to sea level.
P_1=P_2=V_1=V_2=0 . These are very large holding tanks.
Assume minor losses are negligible due to the relatively straight uninterrupted pipeline, which also has a large l/(D=1285591/(1.22=1.05×?10?^6 ))

Now:
h_P=h_L=f l/D V^2/2g

Since the only pressure needed is to push the crude oil through the pipeline overcoming friction.

The Reynolds number for the flow is:


R_e=?VD/µ=(860×2.834×1.22)/?3.83×10?^(-3) =776374


Using the tables e/(D=0.000036) and f=0.0125


h_P=0.0125×1.05×?10?^6 ?2.834?^2/(2×9.81)=5372 m

The power needed to overcome this friction head loss is:


Power=?gQh_P=860×9.81×3.313×5372=150.2 MW

W=J/s=Nm/s=(kgm/(s^2 m))/s=((kgm^2)/s^2 )/s=kg/m^3 ×m/s^2 ×m^3/s×m


Converting this to horsepower gives:


P=355720532/745.69987=201383 horsepower


There are many reasons why it is not practical to drive this flow with a single pump. First there are no pumps this large. Second the pressure at the pump outlet would need to be ?gh_L and no practical 1.22m diameter pipe would withstand this pressure.

The actual system contains 12 pumping stations positioned at strategic locations along the pipeline. Each station contains 4 pumps, 3 of which operate are any one time (the 4th is a backup emergency pump to allow maintenance etc.).
Each pump is driven by one 13,500 horsepower motor; this therefore produces a total output of 486,000 horsepower.
Assuming that the pump/motor combination is approximately 60% efficient there is a total of 292,000 horsepower available to drive the fluid, which compares well with the above calculation.
The assumption of 60oC oil temperature may seem unreasonable for flow across Alaska, however the oil is warm when it is pumped from the ground and the 201,383 horsepower needed to pump the oil is dissipated as a heat loss along the length of the pipeline.
However if the oil temperature were 30oC the viscosity would be approximately twice as large as the value used in the above calculation but the friction factor would only increase from 0.0125 to 0.014. This doubling of viscosity would result in only an 11% increase in the power needed.
Because of the large Reynolds numbers involved, the sheer stress is due mostly to the turbulent nature of the flow. That is the value of Re for the flow is large enough, on the relatively flat part of the Moody chart so that the friction factor is nearly independent of Re (or viscosity).

Alaskan Oil Pipeline

1. Check the efficiency of the pump/motor combination on the Alaskan Oil Pipeline if oil is pumped at the maximum rate and:

• Only the standard 3 pumps are used per pumping station and the 4th remains as a backup.

• All 4 pumps are used at each pumping station.

2. Assuming that the pump/motor combinations are 60% efficient and that the standard 3 pumps are used per pumping station and ignoring any changes in elevation, estimate the maximum horizontal distance between adjacent pumping stations.

3. Draw a simplified longitudinal section of the route of the pipeline and determine where you would locate the pumping stations and indicate these locations on your longitudinal section. Then estimate the pressure head loss along the length of the pipeline and draw a pressure loss graph for the oil pipeline from the Artic ocean to the Valdez terminal

Explanation / Answer

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